When you need to subtract complex numbers, there are some easy rules to follow. This will help you do it without any trouble.

A complex number is usually written like this: (a + bi). Here, (a) is the real part, and (b) is the imaginary part.

Simple Rules for Subtracting Complex Numbers:

1. Find the Parts:
   First, look at each complex number and find the real and imaginary parts.
   For example, with the complex numbers (z_1 = 3 + 4i) and (z_2 = 1 + 2i):

   • (z_1) has a real part of (3) and an imaginary part of (4).
   • (z_2) has a real part of (1) and an imaginary part of (2).

2. Subtract Real Parts:
   Next, subtract the real parts from each other.
   In our example:
   (3 - 1 = 2)

3. Subtract Imaginary Parts:
   Now, do the same for the imaginary parts.
   Using our example:
   (4 - 2 = 2)

4. Put the Results Together:
   Finally, combine what you got from the real and imaginary parts.
   For (z_1 - z_2), we have:
   ((3 + 4i) - (1 + 2i) = (2 + 2i))

If we say it a different way, if (z_1 = a + bi) and (z_2 = c + di), then the subtraction looks like this:
(z_1 - z_2 = (a - c) + (b - d)i)

Another Example:

Let’s try a different example:
If we want to subtract (z_3 = 5 - 7i) from (z_4 = 2 + 3i):

1. Subtract the real parts:
   (2 - 5 = -3)

2. Subtract the imaginary parts:
   (3 - (-7) = 3 + 7 = 10)

3. Finally, put it all together:
   (z_4 - z_3 = (2 + 3i) - (5 - 7i) = -3 + 10i)

Conclusion:

To sum it all up, remember these simple steps when you subtract complex numbers:

• Identify the real and imaginary parts.
• Subtract each part separately.
• Combine the results into one complex number.

Keep practicing with different examples to get better at it!